Solve 2^2-x+2^x=acos(pix)

$$2 ^ { 2 - x } + 2 ^ { x } = a \cos ( \pi x )$$

Solve for a

$$a=\frac{4^{x}+4}{\cos(\pi x)\times 2^{x}}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=n_{1}+\frac{1}{2}$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$a\cos(\pi x)=2^{2-x}+2^{x}$$

The equation is in standard form.

$$\cos(\pi x)a=2^{-x+2}+2^{x}$$

Divide both sides by \cos(\pi x).

$$\frac{\cos(\pi x)a}{\cos(\pi x)}=\frac{2^{-x+2}+2^{x}}{\cos(\pi x)}$$

Dividing by \cos(\pi x) undoes the multiplication by \cos(\pi x).

$$a=\frac{2^{-x+2}+2^{x}}{\cos(\pi x)}$$

Divide 2^{x}+2^{-x+2} by \cos(\pi x).

$$a=\frac{4^{x}+4}{\cos(\pi x)\times 2^{x}}$$